create a s5 modal logic system class in csharp

main.cs
public class S5ModalLogicSystem {
    // Define possible worlds
    private List<World> worlds;

    // Define accessibility relations
    private Dictionary<World, List<World>> relations;

    // Define propositions that are true in each world
    private Dictionary<World, List<string>> propositions;

    public S5ModalLogicSystem() {
        this.worlds = new List<World>();
        this.relations = new Dictionary<World, List<World>>();
        this.propositions = new Dictionary<World, List<string>>();
    }

    // Add a world and its properties
    public void AddWorld(World world, List<string> propList) {
        worlds.Add(world);
        propositions.Add(world, propList);

        // Add reflexive accessibility relation
        List<World> accRels = new List<World> { world };
        relations.Add(world, accRels);
    }

    // Add a directed accessibility relation between two worlds
    public void AddAccessibilityRelation(World from, World to) {
        if (worlds.Contains(from) && worlds.Contains(to)) {
            relations[from].Add(to);
        }
    }

    // Check if a proposition is true in a given world
    public bool IsTrueInWorld(World world, string prop) {
        return propositions[world].Contains(prop);
    }

    // Check if a proposition is true in all worlds accessible from a given world
    public bool IsTrueInAccessibleWorlds(World world, string prop) {
        bool trueInAllWorlds = true;
        List<World> accessibleWorlds = relations[world];

        foreach (World w in accessibleWorlds) {
            if (!propositions[w].Contains(prop)) {
                trueInAllWorlds = false;
                break;
            }
        }

        return trueInAllWorlds;
    }
}

public class World {
    public string Name { get; set; }

    public World(string name) {
        this.Name = name;
    }
}
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